# A particle in Electric and Magnetic field

## Homework Statement

A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

## The Attempt at a Solution

I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?

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Suraj M
Gold Member
What exactly is r"?

What exactly is r"?
r is just position, and by r'' I mean it is r derived twice so that it is acceleration

Suraj M
Gold Member
Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?

Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?
In general it should be F = ma

Suraj M
Gold Member
What would be the shape of the path of the object?

ehild
Homework Helper

## Homework Statement

A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

## The Attempt at a Solution

I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?
Yes, it is correct.
You know the direction of the electric and magnetic field vectors. Write them out in vector form, and determine the components Fx, Fy, Fz of the force. Note that the force depends on the velocity, that is, (x'x, y'y, z'z) , Then you get three equations in the form mx"=Fx, my"=Fy, mz"=Fz.